Compactly supported p-adic pro-étale cohomology of analytic varieties

2025/01/23 by Achinger, Piotr, Gilles, Sally, Nizioł, Wiesława
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.13651

Abstract

We study properties of compactly supported p-adic pro-étale cohomology of smooth partially proper rigid analytic varieties. In particular, we prove a comparison theorem, in a stable range, with compactly supported syntomic cohomology, which is built from compactly supported Hyodo-Kato and \mathcal B⁺_{\rm dr}-cohomologies. We derive from that a (limited version of a) fundamental diagram.

Related

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• Duality for p-adic geometric pro-étale cohomology
• On the cohomology of p-adic analytic spaces, I: The basic comparison theorem
• Duality for Arithmetic p-adic Pro-étale Cohomology of Analytic Spaces
• Rational p-adic Hodge theory for rigid-analytic varieties